Lecture Text Inductor Ckts

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This course is a Virtual Laboratory tutorial in electronics.  Over the last decade,  I have produced a set of free online circuit simulations and animations that constitute a interactive virtual laboratory for students studying electronics or preparing for an IT career .  My virtual interactive circuit troubleshooting exercises cover only a small sample of circuits covered in must texts or college courses. This selection of circuits ranges from simple resistive circuits thru advanced operational amplifiers, digital circuits and computers .   I believe that those who  master troubleshooting my narrow range of virtual circuits or systems will develop the skills necessary to troubleshoot a wide range of circuits and systems that they will be confronted with now and in the future.  I feel quite certain that someone who could not perform the majority of my virtual troubleshooting exercises would be in need of further training in order to become a competent electronics troubleshooter.  This person could benefit from my free virtual laboratory course. 

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Lecture Text Inductor, RCL, and Transformer Circuits


Inductors, RCL Circuits and Transformers.

Simple RL filters work in similar but opposite manner to RC filters.  Replace the capacitor in  a simple RC high pass filter with an inductor and you get an RL low pass filter.  Capacitors are less expensive than inductors, and therefore RC circuits and not RL circuits are generally used to create simple filters.


Complex pass band filters use both inductors and capacitors in conjunction with resistance.  Inductors and capacitors exhibit a property called resonance.  Resistance is normally plotted on the x-axis, capacitance reactance on the positive y-axis and inductive reactance on the negative y-axis.  Resistance and Capacitance reactance form two sides of triangle. The total impedance for a resistor and capacitor in series is the vector sum represented by the triangle hypotenuse. Resistance and inductive reactance form two sides of triangle. The total impedance for a resistor and inductor in series is the vector sum represented by the triangle hypotenuse.  The capacitive reactance phasor points in the opposite direction of the inductive reactance phasor.  Thus, the total reactance along the Y-axis can be determined algebraically.  The method I always used was simple.  First I used my slide rule impedance calculator to determine the capacitance and inductive reactance at the relevant frequency.  If the inductive reactance was greater than the capacitive reactance, then the resultant reactance will be inductive.  If the capacitive reactance were greater than the inductive reactance, then the resultant reactance will be capacitive.  The magnitude of resultant reactance is determined by simple subtraction.

At some frequency the inductance reactance and the capacitance reactance will be equal, and their algebraic sum or vector sum for that matter will be zero.  That frequency is called the resonant frequency.  There is no such thing as a pure  inductor coil, since the coil wire must have some resistance.  Consider a small voltage applied to one end of a capacitor.  The capacitor is connected in series with a coil, and the coils other end is  tied to ground.  As the frequency approaches resonance the combined impedance of inductor and capacitor  becomes very small, and the current  increases towards infinity.  Thus, the voltage drop across the inductor and the capacitor becomes very large. If you connected a high voltage scope probe to the capacitor junction,  you would measure a large voltage.  Note that the high voltage scope probe implies a high resistance probe which will not effect a circuit.  It has been my experience that a times 100 scope probe will usually have an impedance of 100 meg-ohms, and a  times 10 scope probe will usually have an impedance of ten meg-ohms.   

Let us consider the physics of the resonant circuit.  When the voltage reaches a peak, current goes to zero.  Actually, current is at the point of reversal, and all the energy of the oscillation is in the electrostatic field between the capacitor plates. This electrostatic energy is potential energy.  When the capacitor discharges to zero, the current through the coil is at a maximum, and the energy has changed from electrostatic potential energy to magnetic kinetic energy.  This is similar to the operation of a pendulum.  At bottom of a pendulum's arc, the speed and thus kinetic energy is at maximum, and the potential energy of the system is at a minimum.  At the highest point of its arc the pendulum is stationary for the instant that it reverses direction, and thus its kinetic energy is zero.  

Resonance is important in communication, because it is the basis of tuned circuits, oscillators and filters.  A troubleshooter may be tracing a signal expecting it to become large when it is amplified by a transistor or stepped up by transformer.  However, he might be confused by a small signal going to one end of capacitor and coming out the other end many times larger in amplitude.  You may wonder where this large voltage came from and think that some wires must be crossed.  Nothing may be wrong at all, you may just be at the junction of a capacitor and an inductor exhibiting resonance.  I noticed, while observing a complex filter that as the signal went from  input to output that it dipped lower than the final output and at the next stage it jumped much higher than either the input or output.  I was puzzled until I realized that two resonant circuits with different resonant frequencies  were being cascaded to produce band pass filters.  Formula for resonance  is derived below.  Starting with the condition that inductive reactance equals capacitive reactance at resonance, a little algebra gives us the formula to calculate the resonant angular velocity of a LC series circuit or an LC tank circuit.   

A transformer is made starting with an iron ring or other type ferromagnetic ring.  A transformer is produced by winding two or more coils around the ring.  When a AC current is made to flow through the input coil most of the magnetic flux is contained in the ferromagnetic core.  It follows that the same magnetic  flux flows through each coil wound  around this common magnetic core.  Each loop of wire wound around the common core experiences the same rate of flux change as the other loops, and thus the same induced E M F as the other loops.  Thus, the voltage output across each coil will be directly proportional to the number of loops the coil has. No power is generated by a transformer; thus, when the voltage to a circuit is stepped up, the current is stepped down.  The circuit below illustrates this rather well.  Note that changing the location of ground, changes the output of the transformer from one 240 volts output  to two 120 volt outputs.  The 120 volt outputs are 180 degrees out of phase.

My first eBook titled RCL Circuits  has many animations of filter and transformers in it.  You can download it for free.  It is written in the Microsoft Help format, and it requires that you keep two files in the same folder for it to work properly.  Windows Vista will not be delivered with support for the Help format.  You can download the Help Browser from Microsoft.  Windows XP, 2000 and Windows 98 all come with support for Help files embedded in the operating system.   




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Last modified: Monday July 07, 2014.